Should we always control for all available covariates?

Multiple regression provides scientists and analysts with a tool to perform statistical control – a procedure to remove unwanted influence from certain variables in the model. In this section, we’ll discuss different perspectives on statistical control and build an intuition as to why statistical control can easily lead us astray.

Let’s start with an example. When studying predictors of dyslexia, you might be interested in understanding whether parents smoking influences the risk of dyslexia in their children. In your model, you might want to control for parental education. Parental education might affect how much attention parents devote to their children’s reading and writing, and this in turn can impact children’s skills and other characteristics. At the same time, education level might decrease the probability of smoking, potentially leading to confounding. But how do we actually know whether...